# Celliprismated tesseractic tetracomb

Celliprismated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymCapotat
Coxeter diagramx4x3o3o4x ()
Elements
Tera4N tesseracts, 6N square-octagonal duoprisms, 4N truncated cubic prisms, N truncated tesseracts, N small disprismatotesseractihexadecachora
Cells16N tetrahedra, 32N triangular prisms, 8N+24N+24N cubes, 24N octagonal prisms, 8N truncated cubes
Faces64N triangles, 48N+48N+96N squares, 24N octagons
Edges32N+96N+96N
Vertices64N
Vertex figureTriangular antipodial pyramid, edge lengths 1 (small base of antipodium), 2 (sides and other base of antipodium, and lacings to large base), and 2+2 (lacings to small base)
Related polytopes
ArmyCapotat
RegimentCapotat
ConjugateQuasicelliquasiprismated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The celliprismated tesseractic tetracomb or capotat, also called the cellitruncated tesseractic tetracomb or steritruncated tesseractic tetracomb is a convex uniform tetracomb. 1 truncated tesseract, 1 small disprismatotesseractihexadecachoron, 1 tesseract, 3 truncated cubic prisms, and 3 square-octagonal duoprisms join at each vertex of this tessellation. As the name suggests, it is the steritruncation of the tesseractic tetracomb.

## Vertex coordinates

The vertices of a celliprismated tesseractic tetracomb of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}}+(2+{\sqrt {2}})i,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})j,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})k,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})l\right),}$

where i, j, k, and l range over the integers.